John Walsh's delusions by De Morgan

The following is essentially an extract from Augustus De Morgan's A Budget of Paradoxes. We have used the 1915 edition edited by David Eugene Smith and we have included some of Smith's editorial comments in square brackets:

John Walsh of Cork (1786-1847).

[He was born at Shandrum, County Limerick, and supported himself by teaching writing and arithmetic. He died in an almshouse at Cork.]

This discoverer has had the honour of a biography from Professor Boole, who, at my request, collected information about him on the scene of his labours. It is in the 'Philosophical Magazine' for November, 1851, and will, I hope, be transferred to some biographical collection where it may find a larger class of readers. It is the best biography of a single hero of the kind that I know. Mr Walsh introduced himself to me, as he did to many others, in the anterowlandian days of the Post-office; his unpaid letters were double, treble, &c. They contained his pamphlets, and cost their weight in silver: all have the name of the author, and all are in octavo or in quarto letter-form: most are in four pages, and all dated from Cork. I have the following by me:

The Geometric Base, 1825.
The theory of plane angles, 1827.
Three Letters to Dr Francis Sadleir. 1838.
The invention of polar geometry, By Irelandus, 1839.
The theory of partial functions, Letter to Lord Brougham, 1839.
On the invention of polar geometry, 1839.
Letter to the Editor of the Edinburgh Review, 1840.
Irish Manufacture, A new method of tangents, 1841.
The normal diameter in curves, 1843. - Letter to Sir R Peel, 1845.
[Hints that Government should compel the introduction of Walsh's Geometry into Universities.]
Solution of Equations of the higher orders, 1845.

Besides these, there is a 'Metalogia', and I know not how many others.

Mr Boole, who has taken the moral and social features of Walsh's delusions from the commiserating point of view, which makes ridicule out of place, has been obliged to treat Walsh as Scott's Alan Fairford treated his client Peter Peebles; namely, keep the scarecrow out of court while the case was argued. My plan requires me to bring him in: and when he comes in at the door, pity and sympathy fly out at the window. Let the reader remember that he was not an ignoramus in mathematics: he might have won his spurs if he could have first served as an esquire. Though so illiterate that even in Ireland he never picked up anything more Latin than Irelandus, he was a very pretty mathematician spoiled in the making by intense self-opinion.

This is part of a private letter to me at the back of a page of print: I had never addressed a word to him:

There are no limits in mathematics, and those that assert there are, are infinite ruffians, ignorant, lying blackguards. There is no differential calculus, no Taylor's theorem, no calculus of variations, &c. in mathematics. There is no quackery whatever in mathematics; no % equal to anything. What sheer ignorant blackguardism that!

In mechanics the parallelogram of forces is quackery, and is dangerous; for nothing is at rest, or in uniform, or in rectilinear motion, in the universe. Variable motion is an essential property of matter. Laplace's demonstration of the parallelogram of forces is a begging of the question; and the attempts of them all to show that the difference of twenty minutes between the sidereal and actual revolution of the earth round the sun arises from the tugging of the Sun and Moon at the pot-belly of the earth, without being sure even that the earth has a pot-belly at all, is perfect quackery. The said difference arising from and demonstrating the revolution of the Sun itself round some distant centre.

In the letter to Lord Brougham we read as follows:

I ask the Royal Society of London, I ask the Saxon crew of that crazy hulk, where is the dogma of their philosophic god now? ... When the Royal Society of London, and the Academy of Sciences of Paris, shall have read this memorandum, how will they appear? Like two cur dogs in the paws of the noblest beast of the forest. ... Just as this note was going to press, a volume lately published by you was put into my hands, wherein you attempt to defend the fluxions and Principia of Newton. Man! what are you about? You come forward now with your special pleading, and fraught with national prejudice, to defend, like the philosopher Grassi, the persecutor of Galileo, principles and reasoning which, unless you are actually insane, or an ignorant quack in mathematics, you know are mathematically false. What a moral lesson this for the students of the University of London from its head! Man! demonstrate corollary 3, in this note, by the lying dogma of Newton, or turn your thoughts to something you understand.

"Walsh Irelandus."

[Oratio Grassi (1582-1654) was the Jesuit who became famous for his controversy with Galileo over the theory of comets. Galileo ridiculed him in 'Il Saggiatore', although according to the modern view Grassi was the more nearly right. It is said that the latter's resentment led to the persecution of Galileo]

Mr Walsh - honour to his memory - once had the consideration to save me postage by addressing a pamphlet under cover to a Member of Parliament, with an explanatory letter. In that letter he gives a candid opinion of himself:

(1838) Mr Walsh takes leave to send the enclosed corrected copy to Mr Hutton as one of the Council of the University of London, and to save postage for the Professor of Mathematics there. He will find in it geometry more deep and subtle, and at the same time more simple and elegant, than it was ever contemplated human genius could invent.

He then proceeds to set forth that a certain "tomfoolery lemma," with its "tomfoolery" superstructure, "never had existence outside the shallow brains of its inventor," Euclid. He then proceeds thus:

The same spirit that animated those philosophers who sent Galileo to the Inquisition animates all the philosophers of the present day without exception. If anything can free them from the yoke of error, it is the [Walsh] problem of double tangence. But free them it will, how deeply soever they may be sunk into mental slavery - and God knows that is deeply enough; and they bear it with an admirable grace; for none bear slavery with a better grace than tyrants. The lads must adopt my theory. ... It will be a sad reverse for all our great professors to be compelled to become schoolboys in their grey years. But the sore scratch is to be compelled, as they had before been compelled one thousand years ago, to have recourse to Ireland for instruction.

The following "Impromptu" is no doubt by Walsh himself: he was more of a poet than of an astronomer:

Through ages unfriended,
With sophistry blended,
Deep science in Chaos had slept;
Its limits were fettered,
Its voters unlettered,
Its students in movements but crept.
Till, despite of great foes,
Great Walsh first arose,
And with logical might did unravel
Those mazes of knowledge,
Ne'er known in a college,
Though sought for with unceasing travail.
With cheers we now hail him,
May success never fail him,
In Polar Geometrical mining;
Till his foes be as tamed
As his works are far-famed
For true philosophic refining.

Walsh's system is, that all mathematics and physics are wrong: there is hardly one proposition in Euclid which is demonstrated. His example ought to warn all who rely on their own evidence to their own success. He was not, properly speaking, insane; he only spoke his mind more freely than many others of his class. The poor fellow died in the Cork union, during the famine. He had lived a happy life, contemplating his own perfections, like Brahma on the lotus-leaf.

[De Morgan might have found much else for his satire in the letters of Walsh. He sought, in his Theory of Partial Functions, to substitute "partial equations" for the differential calculus. In his diary there is an entry: "Discovered the general solution of numerical equations of the fifth degree at 114 Evergreen Street, at the Cross of Evergreen, Cork, at nine o'clock in the forenoon of 7 July 1844; exactly 22 years after the invention of the Geometry of Partial Equations, and the expulsion of the differential calculus from Mathematical Science.]

JOC/EFR July 2012

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